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   "source": [
    "# How (Not) to Invest III - Beating the Market with Clenow Momentum\n",
    "In the first two posts in this series, I wrote about the MACD, RSI, and Stochastic oscillator, all of which are momentum indicators. In this third post, I write about a less-known indicator: Clenow momentum. In his brilliant book *Stocks on the Move: Beating the Market with Hedge Fund Momentum Strategies*, Andreas Clenow outlines a framework for measuring momentum. His approach involves using an exponential regression to measure the direction and quality of trends. He combines these metrics into a ranking system for choosing the highest momentum stocks at any point in time, and proposes a volatility-based approach to portfolio optimisation.  \n",
    "  \n",
    "Although some claim that Clenow Momentum beat the market, in theory, any publicly available indicator should not. In this post, we evaluate the effectiveness of Clenow Momentum as a trading strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clenow Momentum (CM)\n",
    "  \n",
    "## The Core: Exponential Regression\n",
    "Typically, we would run a simple linear regression of prices on time to estimate how quickly a stock is growing over time. However, that would not be feasible for comparisons across stocks. Hence, Clenow proposes an *exponential* regression in which we run a regression of *log prices* on time. That relates time to *change* in price - and we know that percentage change makes sense for comparisons.  \n",
    "  \n",
    "Clenow proposes a rolling period of 90 days for the exponential regression. Given stock traders' abilities to rapidly react to new information, our measure of CM would need to be much more responsive. Hence, I propose a rolling period of 60 days instead.  \n",
    "  \n",
    "### Component 1: Coefficient of Exponential Regression\n",
    "The first component of Clenow Momentum (CM) measures the trend. In a linear regression of log prices on time, the coefficient  on time essentially tells us the percentage increase in returns for a one-unit change in time (e.g. one day for daily data, 15 minutes for 15-minute data). Clearly, the larger the coefficient, the stronger the trend. To make the coefficient more intuitive, we *annualise* the coefficient.  \n",
    "  \n",
    "### Component 2: R-squared (R2) Measure of Exponential Regression\n",
    "Second, Clenow proposes the R-squared (R2) of the exponential regression as a measure of the quality of the trend. Consider the two scenarios below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import required modules\n",
    "import fix_yahoo_finance as yf\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas_datareader import data as pdr\n",
    "import scipy.stats as ss\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import statsmodels.api as sm\n",
    "import warnings\n",
    "from yahoo_finance import Share\n",
    "\n",
    "# Settings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# Override pdr\n",
    "yf.pdr_override()\n",
    "\n",
    "# Import stocklist\n",
    "sp500 = pd.read_csv('sp500.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create fake data: low R2\n",
    "low_r2 = pd.DataFrame(\n",
    "    {\n",
    "        'a': [1,2,3,4,5],\n",
    "        'b': [1,5,2,4,3]\n",
    "    }\n",
    ")\n",
    "\n",
    "# Create fake data: high R2\n",
    "high_r2 = pd.DataFrame(\n",
    "    {\n",
    "        'a': [1,2,3,4,5],\n",
    "        'b': [1,3,2,3.5,3]\n",
    "    }\n",
    ")\n",
    "\n",
    "a1,b1 = np.polyfit(low_r2.a, low_r2.b, 1)\n",
    "a2,b2 = np.polyfit(high_r2.a, high_r2.b, 1)\n",
    "\n",
    "# Calculate R2 for low R2 data\n",
    "lm_lowr2 = LinearRegression()\n",
    "lm_lowr2.fit(low_r2[['a']], low_r2.b)\n",
    "r2_low = lm_lowr2.score(low_r2[['a']], low_r2.b)\n",
    "coef_low = lm_lowr2.coef_[0]\n",
    "\n",
    "# Calculate R2 for high R2 data\n",
    "lm_hir2 = LinearRegression()\n",
    "lm_hir2.fit(high_r2[['a']], high_r2.b)\n",
    "r2_high = lm_hir2.score(high_r2[['a']], high_r2.b)\n",
    "coef_high = lm_hir2.coef_[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213eee54be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213ef34eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CODE FOR GRAPHICS NOT INCLUDED"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming we have daily data, the slope is 0.30 for Stock A, which suggests that prices are increasing. However, the R2 is extremely low at **9.00%** due to volatility, especially on Day 2. For Stock B, the slope is even steeper, suggesting that prices are rising even faster than Stock A. It also has a lower R2. This means that the line was a much better fit to the data, due to the lower volatility of the stock price *around the general upward trend*. Thus, Clenow suggests that a stock that has a better R2 fit has a lower volatility, and has a higher probability of continuing its trend."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combined Component\n",
    "Clenow posits that both the upward trend and goodness-of-fit are important. Hence, he combines both these measures by **multiplying them**:  \n",
    "  \n",
    "```\n",
    "    Clenow Momentum (CM) = Annualised Slope of Regression Coefficient (%) * R2 of Regression (%)\n",
    "```  \n",
    "\n",
    "## Additional Conditions\n",
    "Clenow slaps on two additional conditions for stock selection. We'll keep this in mind until we test a CM-based trading strategy.\n",
    "  \n",
    "1. **Never invest during a bear market.** The first of Clenow's (declared) additional conditions is to never invest when the market is declining. He does not believe in shorting stocks. Hence, he sets the rule that *if the S&P 500 is trading below its 200-day SMA, do not buy any stocks*.  \n",
    "2. **The stock should be trending upward.** The second additional condition is that the stock should be trading above its 100-day SMA. This is used to quantitatively define an uptrend.  \n",
    "3. **The stock price should be relatively stable.** The third of Clenow's additional conditions is that a stock should not have experienced a 15% or greater jump in price during the lookback period. Although this is implicitly captured under the goodness-of-fit (R2), Clenow implements this condition to ensure that prices are increasing gradually and not experiencing sudden jumps.  \n",
    "  \n",
    "## Stock Selection\n",
    "Clenow proposes updating of portfolios on a weekly basis. On a fixed day each week, CM is calculated for a basket of stocks (the universe), and the stocks are ranked by their CM value. The greater the CM value, the higher the rank. Then, the portfolio is re-balanced. For now, the important thing to note is that the portfolio is updated **weekly** - this helps us to define the look-forward period for our tests: **5 days.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing Clenow Momentum I: Statistical Relationships\n",
    "Clenow posits that the higher the CM score, the higher the probability of continued stock increases over the next 5 days. In this section, we test that assumption by computing the correlation between 5-day forward returns and CM, the R2 of exponential rolling-window regressions, and the slope coefficients of the regressions.  \n",
    "  \n",
    "In our computations, we use an adjusted version of CM (ACM), which incorporates the additional conditions stated above. In any time period where these conditions are not met, ACM is set to zero. ACM therefore represents a simplified version of Clenow's strategy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Fix start date and end date\n",
    "# start_date = '1979-01-01'\n",
    "# end_date = '2018-06-01'\n",
    "\n",
    "# # Pull data\n",
    "# alldata = pdr.get_data_yahoo(list(sp500.Symbol), start_date, end_date, progress=False)\n",
    "\n",
    "# # Pull S&P500 data\n",
    "# sp500_index = pdr.get_data_yahoo('^GSPC', start_date, end_date, progress = False)\n",
    "\n",
    "# # Save data\n",
    "# sp500_index.to_csv('sp500_index.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Save data\n",
    "# alldata.to_csv('sp500_full.csv')\n",
    "# alldata.Close.to_csv('sp500_close.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function for Computing ACM Thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_acm(stk, lookback, full_df):\n",
    "    \n",
    "    # Pull data from main data frame\n",
    "    stock_data = full_df[['days', 'sp500']].copy()\n",
    "    stock_data['close'] = full_df[stk].copy()\n",
    "    \n",
    "    # Remove NaNs\n",
    "    # stock_data.dropna(axis = 0, inplace = True)\n",
    "    \n",
    "    # Run rolling regression with 30-day windows\n",
    "    temp_lm = pd.stats.ols.MovingOLS(\n",
    "        y=np.log(stock_data.close), x=stock_data[['days']],\n",
    "        window_type='rolling', window=lookback, intercept=True\n",
    "    )\n",
    "    \n",
    "    # Compute Clenow Momentum\n",
    "    stock_data['slope'] = ((temp_lm.beta.days + 1) ** 250 - 1) * 100\n",
    "    stock_data['r2'] = temp_lm.r2 * 100\n",
    "    stock_data['cm'] = stock_data.slope * stock_data.r2\n",
    "\n",
    "    # Compute forward returns\n",
    "    stock_data['ret'] = stock_data.close.shift(-5) / stock_data.close - 1\n",
    "\n",
    "    # Compute F1: S&P500 trading above 200-day SMA\n",
    "    stock_data['f1'] = (stock_data.sp500 >= pd.rolling_mean(stock_data.sp500, 200)).astype(int)\n",
    "\n",
    "    # Compute F2: Stock is trading above 100-day SMA\n",
    "    stock_data['f2'] = (stock_data.close >= pd.rolling_mean(stock_data.close, 100)).astype(int)\n",
    "\n",
    "    # Compute F3: Stock has not gapped more than 15% within lookback period\n",
    "    stock_data['roll_max'] = pd.rolling_max(stock_data.close, lookback)\n",
    "    stock_data['roll_min'] = pd.rolling_min(stock_data.close, lookback)\n",
    "    stock_data['inc'] = (stock_data.roll_max > stock_data.roll_min).astype(int)\n",
    "    stock_data['max_gap'] = stock_data.inc * (stock_data.roll_max / stock_data.roll_min - 1) + \\\n",
    "        (stock_data.inc - 1) * (stock_data.roll_min / stock_data.roll_max - 1)\n",
    "    stock_data['f3'] = (stock_data.max_gap < 0.15).astype(int)\n",
    "    \n",
    "    # Compute ACM\n",
    "    stock_data['acm'] = stock_data.cm * stock_data.f1 * stock_data.f2 * stock_data.f3\n",
    "    \n",
    "    # Remove NaNs\n",
    "    stock_data.dropna(axis = 0, inplace = True)\n",
    "    \n",
    "    # Calculate correlation between returns and ACM, R2, and slope\n",
    "    corr_acm = stock_data[['ret', 'acm']].corr().iloc[0,1]\n",
    "    corr_r2 = stock_data[['ret', 'r2']].corr().iloc[0,1]\n",
    "    corr_slope = stock_data[['ret', 'slope']].corr().iloc[0,1]\n",
    "    \n",
    "    # Regression\n",
    "    temp_lm = LinearRegression(n_jobs = 3)\n",
    "    temp_lm.fit(stock_data[['acm', 'r2', 'slope']], stock_data.ret)\n",
    "    \n",
    "    # Extract coefficients\n",
    "    coef_acm = temp_lm.coef_[0]\n",
    "    coef_r2 = temp_lm.coef_[1]\n",
    "    coef_slope = temp_lm.coef_[2]\n",
    "    reg_r2 = temp_lm.score(stock_data[['acm', 'r2', 'slope']], stock_data.ret)\n",
    "    \n",
    "    # Configure output\n",
    "    output = (corr_acm, corr_r2, corr_slope, reg_r2, coef_acm, coef_r2, coef_slope)\n",
    "    \n",
    "    # Output\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# # Reload data\n",
    "# alldata = pd.read_csv('sp500_close.csv')\n",
    "# sp500_index = pd.read_csv('sp500_index.csv')\n",
    "\n",
    "# # Add days\n",
    "# alldata['days'] = np.arange(alldata.shape[0])\n",
    "\n",
    "# # Add S&P500\n",
    "# alldata['sp500'] = sp500_index.Close\n",
    "\n",
    "# # Initialise results list\n",
    "# all_pred = []\n",
    "\n",
    "# # Configure parameters\n",
    "# LOOKBACK = 60\n",
    "\n",
    "# # Subset symbols\n",
    "# symbol_subset = [x for x in list(sp500.Symbol) if x in list(alldata.columns)]\n",
    "\n",
    "# # Loop through stocks\n",
    "# for i in np.arange(0, len(symbol_subset)):\n",
    "    \n",
    "#     # Update\n",
    "#     print('Computing statistics for ' + str(symbol_subset[i]) + ' ' + str(i) + ' of ' + str(len(symbol_subset)) + '...', end = '', flush = True)\n",
    "    \n",
    "#     # Compute thresholds\n",
    "#     temp_thresh = compute_acm(symbol_subset[i], LOOKBACK, alldata)\n",
    "    \n",
    "#     # Append data\n",
    "#     all_pred.append(temp_thresh)\n",
    "    \n",
    "#     # Print results\n",
    "#     print('Done!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Convert to data frame\n",
    "# corr_data = pd.DataFrame(all_pred, columns = [\n",
    "#     'corr_acm', 'corr_r2', 'corr_slope', 'reg_r2', 'coef_acm', 'coef_r2', 'coef_slope'\n",
    "# ])\n",
    "\n",
    "# # Save\n",
    "# corr_data.to_csv('corr_data.csv', index = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the graphs below, we see that on average, there was **no correlation between 5-day forward returns and ACM (which reflects the Clenow Momentum strategy) or the components of ACM: the regression R2 and slope**. The maximum size of the correlation coefficient in either direction (positive or negative) was at most 0.20, which is still relatively small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213eee43898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213ef0eb5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213ef59fc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CODE FOR GRAPHICS NOT INCLUDED"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, we may conclude that statistically, there is no strong relationship between ACM or its components with forward 5-day returns."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Testing Clenow Momentum II: Trading Returns\n",
    "We run a trading simulation using a simplified version of Clenow's approach to test if the strategy beats the buy-and-hold benchmark. The simplified strategy involves the following:  \n",
    "  \n",
    "1. Maintaining an equally-weighted portfolio that is reset every week\n",
    "2. Choosing the top 10 stocks by ACM instead of the top *N* stocks by standard deviation up to a fixed amount in principal\n",
    "  \n",
    "Note that for the CM-based strategy, we only run one simulation because the approach applies to a universe of stocks (in this case the S&P 500). If we wanted confirmation on different universes of stocks, we could easily run the same simulation on the S&P Mid-Cap 400 or the Russell 1000."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Function for Executing Trades"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def trade_acm(stk, lookback, full_df):\n",
    "    \n",
    "    # Pull data from main data frame\n",
    "    stock_data = full_df[['days', 'sp500']].copy()\n",
    "    stock_data['close'] = full_df[stk].copy()\n",
    "    \n",
    "    # Run rolling regression with 30-day windows\n",
    "    temp_lm = pd.stats.ols.MovingOLS(\n",
    "        y=np.log(stock_data.close), x=stock_data[['days']],\n",
    "        window_type='rolling', window=lookback, intercept=True\n",
    "    )\n",
    "    \n",
    "    # Compute Clenow Momentum\n",
    "    stock_data['slope'] = ((temp_lm.beta.days + 1) ** 250 - 1) * 100\n",
    "    stock_data['r2'] = temp_lm.r2 * 100\n",
    "    stock_data['cm'] = stock_data.slope * stock_data.r2\n",
    "\n",
    "    # Compute forward returns\n",
    "    stock_data['ret'] = stock_data.close.shift(-5) / stock_data.close - 1\n",
    "\n",
    "    # Compute F1: S&P500 trading above 200-day SMA\n",
    "    stock_data['f1'] = (stock_data.sp500 >= pd.rolling_mean(stock_data.sp500, 200)).astype(int)\n",
    "\n",
    "    # Compute F2: Stock is trading above 100-day SMA\n",
    "    stock_data['f2'] = (stock_data.close >= pd.rolling_mean(stock_data.close, 100)).astype(int)\n",
    "\n",
    "    # Compute F3: Stock has not gapped more than 15% within lookback period\n",
    "    stock_data['roll_max'] = pd.rolling_max(stock_data.close, lookback)\n",
    "    stock_data['roll_min'] = pd.rolling_min(stock_data.close, lookback)\n",
    "    stock_data['max_min'] = abs(pd.rolling_max(stock_data.close, lookback) / pd.rolling_min(stock_data.close, lookback)) - 1\n",
    "    stock_data['min_max'] = abs(pd.rolling_min(stock_data.close, lookback) / pd.rolling_max(stock_data.close, lookback)) - 1\n",
    "    stock_data['max_gap'] = stock_data[['max_min', 'min_max']].max(axis = 1)\n",
    "    stock_data['f3'] = (abs(stock_data.max_gap) < 0.15).astype(int)\n",
    "    \n",
    "    # Compute ACM\n",
    "    stock_data['acm'] = stock_data.cm * stock_data.f1 * stock_data.f2 * stock_data.f3\n",
    "    \n",
    "    # Output\n",
    "    return (stock_data[['ret']], stock_data.acm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# # Reload data\n",
    "alldata = pd.read_csv('sp500_close.csv')\n",
    "sp500_index = pd.read_csv('sp500_index.csv')\n",
    "\n",
    "# # Add days\n",
    "# alldata['days'] = np.arange(alldata.shape[0])\n",
    "\n",
    "# # Add S&P500\n",
    "# alldata['sp500'] = sp500_index.Close\n",
    "\n",
    "# # Initialise results list\n",
    "# all_ret = pd.DataFrame()\n",
    "# all_acm = pd.DataFrame()\n",
    "\n",
    "# # Configure parameters\n",
    "# LOOKBACK = 60\n",
    "\n",
    "# # Subset symbols\n",
    "# symbol_subset = [x for x in list(sp500.Symbol) if x in list(alldata.columns)]\n",
    "\n",
    "# # Loop through stocks\n",
    "# for i in np.arange(0, len(symbol_subset)):\n",
    "    \n",
    "#     # Update\n",
    "#     print('Computing ACM for ' + str(symbol_subset[i]) + ' - ' + str(i) + ' of ' + str(len(symbol_subset)) + '...', end = '', flush = True)\n",
    "    \n",
    "#     # Compute ACM\n",
    "#     temp_acm = trade_acm(symbol_subset[i], LOOKBACK, alldata)\n",
    "    \n",
    "#     # Append data\n",
    "#     all_ret[symbol_subset[i]] = temp_acm[0]\n",
    "#     all_acm[symbol_subset[i]] = temp_acm[1]\n",
    "    \n",
    "#     # Print results\n",
    "#     print('Done!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compute Returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save data\n",
    "# all_ret.to_csv('ret_data.csv', index = False)\n",
    "# all_acm.to_csv('acm_data.csv', index = False)\n",
    "\n",
    "# Load data\n",
    "all_ret = pd.read_csv('ret_data.csv')\n",
    "all_acm = pd.read_csv('acm_data.csv')\n",
    "\n",
    "# Truncate data by availability: at least 150 stocks to choose from\n",
    "avail_acm = (~all_acm.isnull()).sum(axis = 1)\n",
    "all_ret = all_ret.iloc[364:]\n",
    "all_acm = all_acm.iloc[364:]\n",
    "\n",
    "# Select data for every 5 days\n",
    "all_ret = all_ret.iloc[::5,]\n",
    "all_acm = all_acm.iloc[::5,]\n",
    "\n",
    "# Replace NaNs with zeroes\n",
    "all_acm[all_acm.isnull()] = 0\n",
    "\n",
    "# Rank by row\n",
    "rank_acm = all_acm.rank(axis = 1)\n",
    "\n",
    "# Check for available rankings (at least 1 to 8)\n",
    "rank_avail = rank_acm.apply(lambda x: (x <= 10).sum(), axis = 1) < 8\n",
    "\n",
    "# Convert all rows with unavailable rankings to zero\n",
    "rank_acm[rank_avail] = 0\n",
    "\n",
    "# Convert all ranked stocks (1 to 10) to 1\n",
    "rank_acm[(rank_acm > 0) & (rank_acm <= 10)] = 1\n",
    "\n",
    "# Convert all values above 10 to zero\n",
    "rank_acm[rank_acm > 10] = 0\n",
    "\n",
    "# Get ranks available\n",
    "n_stocks = rank_acm.sum(axis = 1)\n",
    "\n",
    "# Convert zero values to 1\n",
    "n_stocks[n_stocks == 0] = 1\n",
    "\n",
    "# Divide returns by portfolio weight (equal) and add 1\n",
    "all_ret = all_ret.divide(n_stocks, axis = 0)\n",
    "\n",
    "# Convert missing values to zero\n",
    "all_ret[all_ret.isnull()] = 0\n",
    "\n",
    "# Multiply matrices\n",
    "all_profits = all_ret * rank_acm\n",
    "\n",
    "# Sum profits\n",
    "all_profits['total'] = all_profits.sum(axis = 1) + 1\n",
    "\n",
    "# Cumulative profits\n",
    "all_profits['ctotal'] = np.cumprod(all_profits.total) * 100\n",
    "\n",
    "# Add S&P 500\n",
    "all_profits['sp500'] = sp500_index.iloc[364:,].Close[::5] / list(sp500_index.iloc[364:,].Close[::5])[0] * 100\n",
    "\n",
    "# Add date\n",
    "all_profits['Date'] = pd.to_datetime(sp500_index.iloc[364:,].Date[::5])\n",
    "\n",
    "# Change index\n",
    "all_profits.set_index('Date', inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Overall, **the CM-based strategy beat the market**. There were periods where the strategy performed worse than the S&P 500, but the overall drawdowns were significantly lower."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x213ef6ab048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# CODE FOR GRAPHICS NOT INCLUDED"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance of the CM-based strategy and the S&P 500 buy-and-hold benchmark are: (assuming a risk-free rate of 3.00%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strategy</th>\n",
       "      <th>Returns</th>\n",
       "      <th>Volatility</th>\n",
       "      <th>Sharpe Ratio</th>\n",
       "      <th>Max Drawdown</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>CM</td>\n",
       "      <td>8.73%</td>\n",
       "      <td>8.45%</td>\n",
       "      <td>0.677899</td>\n",
       "      <td>-11.67%</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Buy-and-Hold</td>\n",
       "      <td>8.62%</td>\n",
       "      <td>15.03%</td>\n",
       "      <td>0.373798</td>\n",
       "      <td>-27.33%</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Strategy Returns Volatility  Sharpe Ratio Max Drawdown\n",
       "0            CM   8.73%      8.45%      0.677899      -11.67%\n",
       "1  Buy-and-Hold   8.62%     15.03%      0.373798      -27.33%"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute annualised returns\n",
    "annret_cm = (all_profits.ctotal.iloc[-1] / 100) ** (50 / all_profits.shape[0]) - 1\n",
    "annret_sp = (all_profits.sp500.iloc[-1] / all_profits.sp500.iloc[0]) ** (50 / all_profits.shape[0]) - 1\n",
    "\n",
    "# Compute volatility\n",
    "std_cm = (all_profits.total - 1).std() * np.sqrt(all_profits.shape[0] / 50)\n",
    "std_sp = all_profits.sp500.pct_change().std() * np.sqrt(all_profits.shape[0] / 50)\n",
    "\n",
    "# Compute max drawdown\n",
    "maxdd_cm = np.min(all_profits.total - 1)\n",
    "maxdd_sp = all_profits.sp500.pct_change().min()\n",
    "\n",
    "# Configure table\n",
    "sharpe_ratios = pd.DataFrame(\n",
    "    [\n",
    "        {'Strategy': 'CM',\n",
    "         'Sharpe Ratio': (annret_cm - 0.03) / std_cm,\n",
    "         'Returns': '{0:.2f}'.format(annret_cm * 100) + '%',\n",
    "         'Volatility': '{0:.2f}'.format(std_cm * 100) + '%',\n",
    "         'Max Drawdown': '{0:.2f}'.format(maxdd_cm * 100) + '%'},\n",
    "        {'Strategy': 'Buy-and-Hold',\n",
    "         'Sharpe Ratio': (annret_sp - 0.03) / std_sp,\n",
    "         'Returns': '{0:.2f}'.format(annret_sp * 100) + '%',\n",
    "         'Volatility': '{0:.2f}'.format(std_sp * 100) + '%',\n",
    "         'Max Drawdown': '{0:.2f}'.format(maxdd_sp * 100) + '%'}\n",
    "    ]\n",
    ")\n",
    "\n",
    "# Re-order and print\n",
    "sharpe_ratios = sharpe_ratios[['Strategy', 'Returns', 'Volatility', 'Sharpe Ratio', 'Max Drawdown']]\n",
    "sharpe_ratios"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How Did Clenow Momentum Beat the Market?!\n",
    "Thus far, we found no statistically significant relationship between ACM and forward returns. However, we also found that Clenow's strategy beats the market! I propose two theories/potential reasons that explain these results.  \n",
    "  \n",
    "## 1. Momentum Works\n",
    "Momentum is a sustained increase in price because demand outpaces supply. Hence, to make money from momentum, it makes sense to get in on the \"demand side\" as early as possible on a stock that other traders in the market will eventually buy. As long as demand continues to increase, returns for the early buyers will increase. Therefore, **momentum traders must buy stocks that other traders want, before the other traders want them**. This principal incentivises traders to make predictions on the next \"hot stock\", to monitor one another, and jump on the bandwagon as soon as a stock has shown some evidence of positive momentum. Therefore, **momentum works for traders who are able to identify stocks with momentum early enough**.  \n",
    "  \n",
    "This explanation may not have given credit to fundamental factors, but I recognise that fundamental analysis is equally important. The past financial crises have taught us that it is not enough for a stock to have price momentum; the company must have *value-creation momentum* as well. Only fundamental analysis can help us filter stocks that create value.  \n",
    "  \n",
    "## 2. Statistics Assumes a Single, Stable Underlying Relationship\n",
    "In the trading simulation, note how the S&P 500 absolutely slayed the CM-based strategy. Only after the Dot-Com crash (first peak in the green graph) did the strategy start to match the S&P 500. Next, after the 2007 financial crisis, CM destroyed the S&P 500. I am not suggesting the strategy will become even more effective in the years to come. My point is that the relationship between indicators and stock prices change over time. Traditional indicators like MACD and RSI may have worked in the past, but don't work in the modern era. Newer indicators like CM failed in the past, but can now be used to beat the market.  \n",
    "  \n",
    "This phenomenon is related to investor psychology, which has been researched in depth by experts like [Robert Shiller](https://www.nytimes.com/2007/08/26/business/yourmoney/26view.html). On a broader level, stocks demonstrate how people think and survive. We observe how some practices translate to a reward, and we adapt. As more of us start to adapt, we crowd out the rewards. Some of us create new practices that are equally or more rewarding, and others adapt. This cycle causes old relationships (between practices and rewards) to break down, and new relationships to form. Consequently, there is no equilibrium; only efforts to strive toward one. We *invent* an equilibrium retrospectively (using past data) and *then* shape a narrative of it.  \n",
    "  \n",
    "In summary: relationships between indicators and stock prices are never the same...  \n",
    "  \n",
    "* In *different* time periods for the *same* stock\n",
    "* In the *same* time period for *different* stocks\n",
    "* In *different* time periods for *different* stocks\n",
    "  \n",
    "Consequently, traditional statistical tests (which assume some stable underlying relationship) will not be able to identify these relationships."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Limitations\n",
    "This study was limited in several ways. First, we employed a simplified version of Clenow's approach. We did not use Clenow's formula for portfolio re-balancing. Doing so would certainly have affected the portfolio weights. Second, we tested only one configuration: a lookback period of 60 days. Given that trading occurs at a faster pace, it may have been more appropriate to use a shorter lookback period and higher-resolution data. Third, we used only one set of data. I chose the S&P 500 as the universe of stocks that were input into the algorithm. Other more volatile indices like the S&P 400 would have produced different results. I also used daily returns for convenience. The strategy may or may not have been more effective on higher-resolution data. Although a more extensive study would be useful for validating Clenow's approach, the fact that it worked on the S&P 500 shows that it has massive potential."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion [TLDR]\n",
    "In this post, we showed that a strategy using Clenow Momentum **beat the S&P 500 buy-and-hold benchmark**, even though statistical tests showed no significant relation between 5-day forward returns and Clenow Momentum and it's individual components. I propose two explanations for this phenomenon: (1) momentum works and (2) relationships between indicators and stock returns change over time.  "
   ]
  }
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